Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}x-y &= 3 \\ x+3y &= 2\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $x = {-3y+2}$ Substitute this expression for $x$ in the first equation. $({-3y + 2}) - y = 3$ $-3y + 2 - y = 3$ Simplify by combining terms, then solve for $y$ $-4y + 2 = 3$ $-4y = 1$ $y = -\dfrac{1}{4}$ Substitute $-\dfrac{1}{4}$ for $y$ in the top equation. $x+ \dfrac{1}{4} = 3$ $x+\dfrac{1}{4} = 3$ $x = \dfrac{11}{4}$ The solution is $\enspace x = \dfrac{11}{4}, \enspace y = -\dfrac{1}{4}$.